Quality control of an automobile transmission, at a particular manufacturing plant, requires that it passes at least two out of three extreme pressure tests. Let P denote the event that an test is passed, and P be the event that the test is not passed. A given transmission's results can then be characterized by a sequence such as PPP, which means that the third test was not passed, while the first and second tests were passed (this transmission would pass the quality control requirements). a) List the elements of the sample space of all possible outcomes for a transmission. b) List the elements that constitute each of the following events; A: the transmission passes at least one test, B: the transmission passes at least two tests, C: the transmission passes only one test. c) Are A and B disjoint? Why or why not? d) Are B and C disjoint? Why or why not? e) List the elements that constitute each of the following events and describe these events in words (for example, for A, you might say "the transmission fails all three tests"): i) Be ii) Ce iii) AUC iv) An C v) An Bn C vi) (BUC) vii) An A